Heavy Quarkonium States with the Holographic Potential

Defu Hou (CCNU)

From Strings to Things , Seattle , May 2008

With Hai-cang Ren, JHEP 0801:029,2008. 0710.2639 

OUTLINES

Introduction Holographic potential model from AdS/CFT Holographic potential model with IR cut.

Concluding remarks

Many interesting phenomena in QCD lie in the strongly-coupled region.

Non-perturbative methods for analysis

Lattice: problematic with finite chemical potentioal, time-

dependent problems

AdS/CFT: Notable success in RHIC physics

Viscosity, Jet quenching, …

Introduction

QCD Diagramm

Heavy meson melting

• At T<Tc, confined ,potenial linearing rises• At T>Tc, deconf. Short range attraction

range: screening length Lsc

As T , ↗ Lsc , ↘ there exists a Td : the potential no

longer binding for T>Td ( Melting Temperature)

Heavy quakonium melting is an important signal of QGP

Nonperturbative calculation of Td

• Potential model

Lattice F. Karsch , Brambilla…

AdS/CFT Maldacena, Rey, Liu , Avramis

• Spectral function

Lattice Karch

AdS/CFT Hoyos, Kim et al

Holographic potential model from AdS/CFT

Q Qr

1/Tt

Extracting V(r) from Wilson loop

• F(r,t) is the free energy excess of a static pair of qq

The internal energy reads

• F-ansatz

V(r) =F(r,T)

• U –ansatz

V(r)=U(r, T)

Poential From Lattice • Quarkonium probes non-perturbative information about medium. How?

W (C) 1

NTr P exp i A

C

W (C)Texp iLtime E(L) E ren

• Wilson loop is static time-like and in fundamental representation:

• Wilson loop is calculable in lattice QCD

Bielefeld Group, hep-lat/0509001time

distance

L

Ltime

Matsui, Satz 1986

Field Theory Gravity Theory=

Gauge TheoriesQCD

Quantum GravityString theory

the large N limitSupersymmetric Yang Mills

Gravitational theory in 10 dimensions

N large

Calculations Correlation functionsQuark-antiquark potential

Holography

Potential from AdS/CFT

• According to the holographic principle, the thermal average of a Wilson loop operator in 4D N=4 SUSY YM at large N_c and large 't Hooft coupling corresponds to the minimum area of the string world sheet in the 5D AdS metric with a Euclidean signature,

bounded by the loop C, when y goes to infinity, y->1 BH

Minimizing the world sheet area (the Nambu-Goto action)

qq r qq r

BH

+_

y

Free energy

Result of pentential

Bound state & Schrődinger equation

Numerical Results

• Value of ‘t Hooft coupling.

• Upper limit : QCD value of coupling at RHIC

• Lower limit: heavy quark potential , (Gubser)

• Mc=1.65Gev, Mb=4.85Gev, Tc=186MeV

Dissociate Temperature

Td in MeV

Holographic potential model with an IR cutoff

Hard Wall : Erlich, Katz, Son, Stephanov

• In the hadronic phase

• In the plasma phase

• Soft-wall model 1 : Karch, Katz, Son, Stephanov

A dilaton is introduced, Metrics are the same.

• Soft-wall model 2 : Andreev,Zakharov;Kajantie

modify string frame metric by a conformal factor

• Free energy

Td with deformed metric

AdS/CFT and Lattice

Summary

To assess the validity . At melting temperature of U satz

We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential

The computed Td have remarkable features compariable with that from Lattice

Thanks for your attention!